A generating function, or Molien function, the coefficients of which give the number of independent polynomial invariants in G, has been useful in the Landau and renormalization group theories of phase transitions. Here a generalized Molien function for a field theoretical Hamiltonian (with short-range interactions) of the most general form invariant in a group G is derived. This form is useful for more general renormalization group calculations. Its Taylor series is calculated to low order for the FGamma-2 representation of the space group R[3 bar]c and also for the l=1 (faithful) representation of SO(3).
(c) 1985 American Institue of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics and may be found at http://link.aip.org/link/?JMAPAQ/26/1442/1;